Post on 05-Jan-2016
Advanced Numerical Modelling of the PHOENIX-SPES charge
breederA. Galatà1, D. Mascali2, L. Neri2, G. Torrisi2, and L. Celona2
1INFN - Laboratori Nazionali di Legnaro, Viale dell’Università 2, 35020 Legnaro (Padova), Italy2INFN - Laboratori Nazionali del Sud, Via S. Sofia 62, 95123 Catania, Italy
Outline
• Description of SPES and its Charge Breeder.
• Background theory and its numerical implementation.
• The code and its results.
• Conclusion and perspectives.
Cyclotron: p 70MeV, 750μA
Radio Frequency Quadrupole-Cooler
High Resolution Mass Spectrometer (1/20000)
Post-Acceleration: new RFQ+ALPI
• Up to 1013 proton induced fissions/s; A = 80 ÷ 160
ECR-based Charge Breeder
• Production, Ionization and Post-Acceleration of Radioactive Species
Target-Ion-Source system
The SPES Project
Target-Ion-Source system
SPES: ECR-based CB (SPES-CB)
• Upgraded version of Phoenix by LPSC.
• Agreement signed in June 2014.
• Acceptance tests in Spring 2015 (see ThuPE26).
• Delivery at LNL in Autumn 2015 .
EFFICIENCY* [%]
ION Q SPES req
Best LPSC
SPES-CB
Cs 26 ≥ 5 8,6 11,7Xe 20 ≥ 10 10,9 11,2Rb 19 ≥ 5 6,5 7,8Ar 8 ≥ 10 16,2 15,2*results obtained for the same 1+
injected current
Optimized position of iron rings
New extraction system
Almost all metal sealings
SPES-CB performances
• The performances of Phoenix got better during the years.
• Room for improvements still exists (gaseous Vs condensable).
• Previous work by M. Cavenago et al.
Numerical simulations can be a powerful tool to optimize the charge breeding process
Here we present a new numerical approach to the charge breeding process, with the analysis of the influence of different beam and plasma parameters
ECR-based charge breeding process
• Focusing.
• Deceleration (V,B).
• Interaction with the plasma.
• Creation and destruction of charge states: Step-by-step ionizations. Charge reduction (charge exchange, electron
capture...). In common with conventional sources.
Multiple Coulomb collisions
ECR-CB peculiarity
CsCharge breeding
Thermalization
Background theory of Coulomb collisions
• Chandrasekhar (General), Spitzer (Charged Particles).
• Collisions are described by the Fokker-Plank equation.
• The coefficients are determined supposing a background of thermal ions.
Perp. diffusion: <(Δv⊥)2>=D⊥ Par. diffusion: <(Δv//)2>=D//
τs τD τE
90° Degree Deflection Energy ExchangeSlowing Down
Characteristic times
Dynamical Friction: <Δv//>
• Equations
• Trends
• Limits
Φ-GG
Always increasing
Similar to ΔV
v0: no friction; isotropic diffusion v∞: transversal diffusionHeavy particles dominated by friction
Friction and Diffucion Coefficients
Implementation of Coulomb collisions
• Forward Difference method:
• MC approach fails Langevin Formalism
v(t+1)=v(t) + a*Tstep x(t+1)=x(t)+ v*Tstep
ΔvLang= v(t+1)-v(t)= - νsv(t)*Tstep+vrand
Slowing down Diffusion
Friction: a=- νsvRandom vector vrand
A benchmark for the code: case study
• Rb charge breeding within EMILIE* Optimum ΔVopt ~ -12 V. Global capture < 50%.
• Anomalous ΔV curves for Rb1+
Rb1+ efficiency some % @ ΔVopt. Efficiency increases with ΔV.
• Weakly interacting 1+ ions Rb1+ cb time plasma on and off τcb: 500 μs
NUMERCAL SIMULATIONS GOALS• Reproduction of Rb1+ ΔV curve• Tspan= 500 μs
• Global capture≥ 40 % @ ΔVopt ~ -12 V
• Rb1+ efficiency few % @ ΔVopt ~ -12 V*O. Tarvainen et al, PSST (2015), 24 035014
*Thanks to J. Angot and T. Lamy
VCB2 EinzelRb1+ @ 20 keV
plasma
VP
SIMION CODE
• Starting conditions Simulation of Rb1+ injection in experimental conditions. Characterized by Einj=E-Vp*q → ΔVsim=Vp-E/q. ΔVexp=VCB-E/q < ΔVsim (plasma potential?)
Input parameters
• Geometry: Cylinder l=288 mm r=36 mm between magnetic filed maxima. Injection, radial and extraction losses. If lost at extraction but r<4→extracted.
2/8.617
)(
)22(2)('2
2)('2
mTS
zpBz
yxSzpy
yB
Sxyzpx
xB
Ions starting conditions for the numerical code
Analytical formulas for the magnetic field components
Simulated curves will be allowed to shift towards more negative ΔV
Plasma modeling
• BASIC PLASMA MODEL (BPM)plasmoid/halo scheme (nhalo=nplasmoid/100)Boris method for B motionlosses
v(t+1)-v(t)=ΔvLang + a*Tstep (Tstep=100 ps)plasma
Rb1+ @ different Einj
v(t+1)-v(t)= ΔvLang + q/m[E+v(t)xB] *Tstep
nplasmoid
nhalo
Becr
v(t+1)-v(t)= ΔvLang + q/m[v(t)xB] *Tstep
• COMPLETE PLASMA MODEL (CPM) Potential dip for electrostatic ion confinement. Complete Lorentz force. nwarm=ncold/10, nwarm distributed as ncold
KTwarm=1/0.1 keV, ionizations (Lotz) Tabulated values for τioniz(q) Ionization applied through MC
Loads starting conditions
Collocates the particles inside or outside the resonance, solves the Langevin equation and applies the Boris
method
Stores the entire workspace on a file
Updates positions and velocities that become the starting conditions for the next iteration
YesChecks
for saving
Removes them from the
calculation
No
Checks for losses
Stores their positions and
velocities
Yes
No
BPM: flow diagram
BPM: results @ KTi=1 eV
• Capture is low, independent from n and weakly on Einj
• Ions residence time: plasma state?→υcoll Vs υcycl
υcoll ≤ υcycl all n
Magnetic Regime
ncore=i*nco
Einj = 2:5:22 eV •nco=2.6∙1018 m-3
•i=1, 0.6, 0.3, 0.1•<z>=2.5
•τmag=Rl/vT ~ 400-600 μs
•Agreement with Tspan
•τmag independent from n
1000 Rb1+ ions
BPM: results @ KTi=0.376 eV
• Overall confinement increased
• Different behaviour between low and high density
υcoll Vs υ cycl
υcoll <~ υ cycl @ low dens (see KT=1 eV)
υcoll > υ cycl high dens → Collisional Regime
Hardly applicable to 1+ ions!
ncore=i*nco
Einj = 2:5:27 eV •nco=2.6 ∙1018 m-
3
•i=1, 0.6, 0.3, 0.1•<z>=2.5
1000 Rb1+ ions
BPM: Rb1+ efficiencyKT=1 eV KT= 0.376 eV
For both temperatures no Rb1+ ions extracted unless n<0.3*nco
Similar trends but no agreement
BPM: summary
• KTi is a key parameter for a good capture.
• KTi has to be low (0.376 eV) in order to have a capture comparable with experiments.
• no Rb1+ efficiency unless n<0.3*nco.
KT=1 KT=0.376
Magnetized plasmafor all n
Low confinement
Constant losses for all
energies
High n Low n
Collisional plasma
Magnetized plasma
Optimum injection energy
Higher capture than high n and KT=1
Higher confinement
Weaker frictional force at the lowest density
Plasma Temperature
Loads starting conditions
Collocates the particles inside or outside the resonance, solves the Langevin equation and applies the Boris
method
Stores the entire workspace on a
file
Updates positions and velocities that become the starting conditions for the next iteration
YesChecks
for saving
Removes them from the calculation
No
Checks for losses
Stores their positions
and velocities
Yes
No
CPM: flow diagram
Checks for ioniz
Yes
No
q=q+1
BMP
+ po
tent
ial d
ip +
ioni
zatio
ns
CPM Vs BPM @ KTi=1 eV and nco
Capture increases up to a factor > 3 Ionizations take place
CPM: KTi=0.376 eV and n=0.1nco
The capture is still too low Rb1+ efficiency agrees with experiments
n=0.1*nco
Einj [eV] Losses [%] Captures [%] ε1+ [%]
2 59.70 44.62 0.16
7 60.80 39.93 0.64
12 58.00 18.70 11.68
17 59.80 3.20 27.76
22 59.60 0.40 44.72
Requirements not completely fulfilled yet
CPM: refinements
n=0.1*nco n=0.075*nco
<z>=3 from a spectrum supposed ΔE=2 eV for Rb1+ beam KTi=0.3 eV
Shift -1.5 V
Shift -4 V
Einj [eV] Captures [%] ε1+ [%] ΔVsim [V]
10 44.71 2.16 -11.5
Einj [eV] Captures [%] ε1+ [%] ΔVsim [V]
7 47.64 0.80 -11
10 39.51 9.28 -14
GOALS ACHIEVED !
Distribution of captured particles Ionizations Distribution of losses
Most of the particles are within the plasmoid
First ionizations take place in agreement with the estimated ionization times Losses are mostly radial
CPM: details for n=1.95∙1017 m-3; ΔVsim= -11V
DENSITY MAP
10 eV 15 eV
resonance
2 eV 5 eV
THE OPTIMUM INJECTION ENERGY IS
EVIDENT
CPM: details for n=1.95∙1017 m-3; ΔVsim= -11V
• Injected particles release energy inside the plasma.
• The effect on the plasma can be experimentally observed
Xe injection
resonance
CPM: details for n=1.95∙1017 m-3; ΔVsim= -11V
Oxygen CSD
HIGHLY LOCALIZED ENERGY RELEASE
Conclusions
• Slowing down and capture correctly implemented in a single particle approach: Model of increasing complexity. Agreement with theorectical expectations. Agreement with experiments for a narrow set of plasma parameters.
• Important outputs: Key role of ion temperature. Density estimation in agreement with experimental results within EMILIE. Energy deposition map.
• Predictive tool for the capture process: Influence of beam emittance. Influence of ion mass. Information about RIBs losses
• Improvement of the plasma-target model:• Electromagnetic calculations (see ThuPE27).• ECR heating and Coulomb collisions.• Self consistent calculations of the electron density map.• Warm electrons density estimations.
• Multipurpose Simulation Tool• ECRIS (ECR-CB) and MDIS• Implementation of several processes (Coulomb, ioniz., excit., ecc..)• External electromagnetic fields (static, variable)
Perspectives
(TuePE11)
A lot of work to do!!!
THANK YOU VERY MUCH FOR YOUR
ATTENTION